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by vineetbatra » Sun Jun 21, 2009 4:30 pm
At a certain university, the ratio of the number of teaching assistants to the number of students in a course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants.

130, 131, 132, 133, 134

My reasoning is that the ratio should be atleast 3:80 (always greater than). If instead of 3 we have 5 assiatant then the exact value is 133.33, however since we have to find the maximum number of students per teacher, where the ratio should be atleast 3:80 the answer has to be more than 133.33, the given max is 134, so i selectd E.

The answer is d. Can someone tell me the flaw in my reasoning.
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by Robinmrtha » Sun Jun 21, 2009 6:43 pm
given,
the number of students in a course must always be greater than 3:80
i.e....
t/s=3/80
this means for 80 students there must be at least 3 teaching assistants.
or 3 teaching assistant can only teach at most 80 students..
1 teaching assistant can only teach at most 80/3 students
5 teaching assistants can only teach at most 80/3 x 5 students = 133.3..
so, as per the question the number of students that the 5 teaching asst can teach must be below 133.33 but not more than 133.33...
So 133 is the answer...
(D)
Hope this helps
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by avanishjoshi » Sun Jun 21, 2009 11:27 pm
As the denominator value increases the value of the ratio decreases.So once should choose the value in the lower range.So the answer is 133.
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by avanishjoshi » Sun Jun 21, 2009 11:30 pm
As the denominator value increases the value of the ratio decreases.So once should choose the value in the lower range.So the answer is 133.
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cross check

by pops » Mon Jun 22, 2009 1:27 am
For 134 students you should have
134*3/80 = 5.025 TAs (i.e. more than 5)

so 5 TAs can take care of 133 students
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by vineetbatra » Mon Jun 22, 2009 4:08 am
Thanks for the responses guys, I understand all you say but please explain the following part of the Q

"the ratio of the number of teaching assistants to the number of students in a course must always be greater than 3:80"

the bold part says that ratio should always be greater than 3:80, so it can be greater than 3:80 but not less, if we take 133 then the ratio is less than 3:80, it will be 3:79.8. this is the part that I do not really understand.
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by kidcorpo » Mon Jun 22, 2009 5:57 am
vineetbatra wrote:Thanks for the responses guys, I understand all you say but please explain the following part of the Q

"the ratio of the number of teaching assistants to the number of students in a course must always be greater than 3:80"

the bold part says that ratio should always be greater than 3:80, so it can be greater than 3:80 but not less, if we take 133 then the ratio is less than 3:80, it will be 3:79.8. this is the part that I do not really understand.
Yes, look at the following:
3/80 = 0.0375
3/79.8 = 0.03759

0.03759 > 0.0375, therefore 3/79.8 is GREATER that 3/80, thus satisfying the original question!
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